Exam May 2015, questions PDF

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Faculty of FET. Academic Year: Examination Period: Module Leader: Module Code: Module Title: Work Item Code: Duration:

14/15 January

Quan Zhu UFMFW7-15-3 CONTROL SYSTEMS DESIGN CC1 2 Hours

Standard materials required for this examination: Examination Answer Booklet

Yes

Multiple Choice Answer Sheet

No

Graph Paper

Type of paper e.g. G3, G14

G3

Number of sheets per student

1

Additional materials required for this examination: Details of additional material supplied by UWE:

To be collected with Answer Booklet (please delete as appropriate)

No

Details of approved material supplied by Student: To be collected with Answer Booklet (please delete as appropriate)

No

University approved Calculator Candidates permitted to keep Examination Question Paper

Candidates are NOT permitted to turn the page over until the exam starts

Instructions to Candidates: Answer FOUR questions from SIX. All questions carry EQUAL marks. QUESTION 1 [Total Marks 25] UFMFW7-15-3

Page 1 of 7

Consider a typical electrical system, its LRC circuit shown in Figure Q1. The circuit consists of an inductor of value L (henry), a resistor of value R (ohm), and a capacitor of value C (farad). The input is the supplied voltage ei and the output is the voltage drop cross the capacitor eo .

Figure Q1 The tasks for the dynamic system modelling and performance evaluation are specified below. 1) Applying Kirchhoff’s voltage law or the other principles to derive the inputoutput dynamic model equation. [7 marks] 2) Applying Laplace transform to determine the model transfer function, and then formulate the undamped nature frequency and damping ratio in terms of L, R, and C. [8 marks] 3) While L=1, R=3, and C=0.5, determine the system output time response to a unite step input, by inversing the output transfer function with reference to the following formula or any other approaches you are familiar with. [7 marks]









  d m 1  1 ( s  si ) m F ( s)e st  f (t ) L 1  F ( s)  Re s F ( s)e st    1 m      s s  m 1 ! ds  i

4) While L=1, R=3, and C=0.5, analyse the system stability. [3 marks]

UFMFW7-15-3

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QUESTION 2 [Total Marks 25] A simplified suspension system for an aircraft landing gear is shown in Figure Q2 R(s)

+ -

k1 s (s  2)

Y(s)

1  k2 s

Figure Q2 where k 1 and k2 are constant gains. The task is to analyse and design the control system as specified below: 1) Workout the closed loop transfer function. [6 marks] 2) Design the control system by selecting gains k 1 and k2 such that it has a damping ratio  of 0.5 and undamped natural frequency n of 4 rad/sec. [8 marks] 3) Determine the poles and zeros of the designed closed loop transfer function and show their positions on S plane. [5 marks] lim f (t )  lim sF (s ) ) determine the 4) With reference to the final theorem ( t   s 0 designed system output steady state response to a unite step stimulation. [6 marks]

UFMFW7-15-3

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QUESTION 3 [Total Marks 25] A typical DC (Direct Current) motor voltage-speed model as shown in Figure Q3 has been identified as the 1 st order transfer function below

 (s ) 2/3  E ( s) s  1/ 3 where  is motor speed and E is the supplying voltage. The tasks to analyse the system are specified below 1) Identify the values of time constant, gain, and pole and briefly discus the functions of time constant, gain and pole. [7 marks] 2) Determine its frequency response transfer function in terms of its amplitude and angle. [6 marks] 3) Calculate the amplitude and phase shift at its corner frequency. [6 marks] 4) Plot the approximate Bode diagrams of the transfer function. [6 marks]

In p u t E ( v o lts )

P o w er A m p lif ie r

DC m o to r

O u tp u t S h a ft

V e lo c it y  R a d /s

1 /s

O u tp u t  ( R a d ia n s )

T acho

K t K r Figure Q3

UFMFW7-15-3

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QUESTION 4 [Total Marks 25] Liquid level systems are frequently used in paper mills. A typical two tank system is shown in Figure Q 4, in which Qi and Qo are the inflow rate and outflow rate respectively, H 1 and H2 the liquid levels of tanks 1 and 2 respectively. The correspondent controllable state space description has been obtained as 1  0 A    8  6

0  B    C  2 1 D 0 1 

1) Identify the plant state equation, output equation, dynamic order, numbers of input and output. Briefly explain the function of the matrices A, B, C, and D. [7 marks] 2) Determine the Laplace transfer function Qo(s)/Qi(s). [7 marks] 3) Determine the system controllability [7 marks] 4) Determine the system observability. [4 marks]

control valve Qi

load valve H1

load valve H2

Qo

Figure Q4

UFMFW7-15-3

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QUESTION 5 [Total Marks 25] A simplified UAV (Unmanned Ariel Vehicle, shown in Figure 5) dynamic model has been identified below  0 1 A     2  3

 0 B    1

C  1 0

D 0

A state feedback controller is designed with the desired poles at ( s)  s  4  s  1 s 2  5 s  4 and achieves zero steady error to a unit step input. 1) Design to confirm the state feedback gain matrix F s  f1  ( s ) det sI  A  BF s  compared

f 2     2  2  by

with ( s)   s  4   s  1  s  5 s  4 . [9 marks] 2



2) Design to confirm the forward gain matrix H= 4 by H  C  A  BFs   1 B marks]



1

. [7

3) Determine the output relationship of the controller output (assumingly it is u (t ) ) with state vector (assumingly it is x(t ) ) and reference (assumingly it is v(t ) ) plus the designed state feedback gain matrix Fs and the forward gain matric H. [5 marks] 4) Explain why the output response is characterised with the monotonic behaviour. [4 marks]

Figure 5

UFMFW7-15-3

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QUESTION 6 [Total Marks 25] The state space model of a DC (Direct Current) servomotor is given as follows. In case of no transducer to measure speed signal, it is required to design a full order identity observer for implementing the control of the angular displacement and velocity in rotation.

1   0 A     6  5

 0 B    1

C 1 0

D 0

In the observer design, the poles of the observer are required to lie at s = -6 and s = -1. The requested tasks are listed below. 1) Determine matrix N by Specified observer polynomial det[ sI  ( A  NC)] . [7 marks] 2) Determine matrix M by M  ND  TB 0 T identity matrix [4 marks] 3) Determine matrix L by NC  TA  LT 0 T identity matrix . [7 marks] 

4) Present the designed observer in terms of L, M, N, X ( t ) , u(t), and y(t). [7 marks] END OF QUESTION PAPER

UFMFW7-15-3

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